Stochastic Simulation Methods for Solving Systems with Multi-State Species

Gillespie's stochastic simulation algorithm (SSA) has been a conventional method for stochastic modeling and simulation of biochemical systems. However, its population-based scheme faces the challenge from multi-state situations in many biochemical models. To tackle this problem, Morton-Firth and Bray's stochastic simulator (StochSim) was proposed with a particle-based scheme. The thesis first provides a detailed comparison between these two methods, and then proposes improvements on StochSim and a hybrid method to combine the advantages of the two methods. Analysis and numerical experiment results demonstrate that the hybrid method exhibits extraordinary performance for systems with both the multi-state feature and a high total population.

In order to deal with the combinatorial complexity caused by the multi-state situation, the rules-based modeling was proposed by Hlavacek's group and the particle-based Network-Free Algorithm (NFA) has been used for its simulation. In this thesis, we improve the NFA so that it has both the population-based and particle-based features. We also propose a population-based method for simulation of the rule-based models.

The bacterial chemotaxis model has served as a good biological example involving multi-state species. We implemented different simulation methods on this model. Then we constructed a graphical interface and compared the behaviors of the bacterium under different mechanisms, including simplified mathematical models and chemically reacting networks which are simulated stochastically.